Question

$\frac{1}{4}$$[\sqrt{3}cos{23}^{\circ }-sin{23}^{\circ }]$ =

• A. cos43⁰
• B. cos7⁰
• C. cos53⁰
• D. None of these

Answer 1

The correct option is D

None of these

$\frac{1}{4}$$\sqrt{3}cos{23}^{\circ }-sin{23}^{\circ }$

= $\frac{1}{2}$$cos{30}^{\circ }cos{23}^{\circ }-sin{30}^{\circ }sin{23}^{\circ }$

= $\frac{1}{2}$ $cos({30}^{\circ }+{23}^{\circ })$ = $\frac{1}{2}$ $cos{53}^{\circ }$.